Here's the story behind House Stark's origin in Game of Thrones. House Stark of Winterfell was one of the Great Houses of Westeros and the true rulers of the North. The House has been around since the Age of Heroes and was at the center of much of the conflict present in Game of Thrones.
During the series, Eddard Stark was introduced to be the head of House Stark as well as the Lord of Winterfell. The castle of Winterfell was where the noble family resided since the House was founded. Following Ned's death, his eldest son, Robb, was named King in the North. It had been the first time since Aegon Targaryen's conquest that a Stark took the title of King. The Starks rule of the North briefly came to an end at the hands of House Bolton, but following the Battle of the Bastards, Jon Snow helped House Stark regained their royalty and was crowned King in the North, a title he'd renounce when he bent the knee to Daenerys Targaryen. In the end, the leadership fell to Sansa when she was named Queen of the North, with Winterfell as an independent kingdom.
The Starks have one of the longest lines of nobility in Game of Thrones history. House Stark descended from the First Men, the group that initially migrated to the continent. Brandon Stark, a member of the First Men, served as the founder of House Stark. When he developed the Great House, the ancestors of House Dustin of Barrowton ruled the North. Bran went on to build a number of notable structures including the Wall and Winterfell, which gave him the nickname "Bran the Builder." He may have also had a part in constructing Storm's End according to the legend. The house sigil featured a direwolf and their motto was a warning rather than a threat: "Winter Is Coming."
After thousands of years, House Stark took control of the North by forcing their rivals out of the territory. Before the Targaryen conquest, the son of the King in the North, Karlon Stark, was awarded the eastern region of the North where he developed a new territory. Those that descended from Karlon became known as the Karstarks, a key ally to House Stark. During the conquest, the King in the North at the time, Torrhen Stark, bent his knee to the Targaryens which was when they changed their title to Wardens of the North.
After the execution of Rickard Stark by the Mad King, Aerys II Targaryen, Robert's Rebellion broke out which proved to be the collapse of the Targaryen dynasty. House Stark ended their allegiance with the Targaryens and became aligned with House Baratheon when Robert Baratheon took over the Iron Throne. When Game of Thrones began, Ned Stark was named the Hand of the King to King Robert Baratheon. That position would go on to be short-lived after both men were killed, jumpstarting the War of the Five Kings and pitting many Great Houses against each other.